Explain the Error

Polly’s parents’ car weighs about 3500 pounds. Samantha, Esther, and Polly each wrote the weight of the car in scientific notation. Polly wrote \(35.0 \times 10^ 2\) , Samantha wrote \(0.35 \times 10^ 4\) , and Esther wrote \(3.5 \times 10^ 4\) .

a. Which of these girls, if any, is correct?

b. Explain the mistakes of those who got the question wrong.

Justify Reasoning

If you were a biologist counting very large numbers of cells as part of your research, give several reasons why you might prefer to record your cell counts in scientific notation instead of standard notation.

Draw Conclusions

Which measurement would be least likely to be written in scientific notation: number of stars in a galaxy, number of grains of sand on a beach, speed of a car, or population of a country? Explain your reasoning.

Analyze Relationships

Compare the two numbers to find which is greater. Explain how you can compare them without writing them in standard notation first.

\(4.5 \times 10^ 6 \)              \( 2.1 \times 10^ 8\)

Communicate Mathematical Ideas

To determine whether a number is written in scientific notation, what test can you apply to the first factor, and what test can you apply to the second factor?